Answer:
11.3 g
Explanation:
given,
density of the lead = 11.3 g/cm³
volume = 1 cm³
mass of the lead = ?
we know,
mass = volume x density
mass = 1 x 11.3
mass = 11.3 g
hence, the mass of the lead is equal to 11.3 g
Examples of structure or machine parts that may fail due to bending
1 answer:
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The air drag is a force that depends on the speed of an object relative to the wind. Under certain conditions, it can be modeled as:
Where b is a constant.
As a falling object reaches a speed so that its weight is cancelled out by the air drag, the object will reach a maximum velocity.
In a speed vs time gaph, the speed would approach the maximum speed like an asymptote.
On the other hand, since the object falls from rest, the initial speed on the graph must be zero.
Taking these considerations into account, the correct graph for the movement of an object that falls from rest if air drag is not ignored, is option B.
Answer:
a)
b)
c)
Explanation:
The very first thing we must do in order to solve this problem is to find an equation for the simple harmonic motion of the given particle. Simple harmonic motion can be modeled with the following formula:
where:
A=amplitude
= angular frequency
t=time
we know the amplitude is:
A=5.0cm
and the angular frequency can be found by using the following formula:
so our angular frequency is:
so now we can build our equation:
we need to find the speed of the particle when it is 3m from the centre of its motion, so we need to find the time t when this will happen. We can use the equation we just found to get this value:
so we solve for t:
you can directly use this expression as the time or its decimal representation:
t=0.81933
since we need to find the speed of the particle at that time, we will need to get the derivative of the equation that represents the particle's position, so we get:
which simplifies to:
and we can now substitute the t-value we found previously, so we get:
so its velocity at that point is cm/s
b) In order to find the maximum velocity we just need to take a look at the velocity equation we just found:
its amplitude will always give us the maximum velocity of the particle, so in this case the amplitude is:
so:
c) we can use a similar procedure to find the maximum acceleration of the particle, we just need to find the derivative of the velocity equation and determine its amplitude. So we get:
We can use the chain rule again to find this derivative so we get:
so when simplified we get:
its amplitude is:
so its maximum acceleration is: